If one of the lines represented by $2{\mathrm{x}}^2+2\mathrm{hxy}+3{\mathrm{y}}^2=0$ be perpendicular to one of the lines given by $3{\mathrm{x}}^2-2{\mathrm{h}}^{\text{'}}\mathrm{xy}+2{\mathrm{y}}^2=0$, then

detailed solution

Correct option is B

Suppose that y=mx is one of the lines represented by the equation 2x2+2hxy+3y2=0It implies that 3m2+2hm+3=0                                                    …… (1)Since, equation of the line perpendicular to the line y=mx is y=−1mx Suppose that y=−1mx is one of the lines represented by the equation 3x2−2h'xy+2y2=0 It implies that 2m2−2h'm+3=0                                                  …… (2)Comparing the above two conditions,⇒h+h'=0since,m≠0